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Late time evolution of negatively curved FLRW models

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Abstract

We study the late time evolution of negatively curved Friedmann–Lemaître–Robertson–Walker (FLRW) models with a perfect fluid matter source and a scalar field nonminimally coupled to matter. Since under mild assumptions on the potential V, it is already known—see e.g., Giambò and Miritzis (Class Quantum Grav 27:095003, 2010)—that equilibria corresponding to nonnegative local minima for V are asymptotically stable, we classify all cases where one of the energy components eventually dominates. In particular for nondegenerate minima with zero critical value, we rigorously prove that if \(\gamma \), the parameter of the equation of state is larger than 2/3, then there is a transfer of energy from the fluid and the scalar field to the energy density of the scalar curvature. Thus, the scalar curvature, if present, has a dominant effect on the late evolution of the universe and eventually dominates over both the perfect fluid and the scalar field. The analysis in complemented with the case where V is exponential, and therefore the scalar field diverges to infinity.

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Notes

  1. Also observe that the transition case \(\gamma =\tfrac{2}{3}\) is excluded from the current analysis, similarly to the transition case \(\gamma =1\) of [20, Theorem 2].

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Acknowledgements

The authors wish to thank Salvatore Capozziello and Orlando Luongo for valuable discussions and suggestions. We also thank an anonymous referee for his suggestions which helped us to clarify some points.

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Author notes

  1. Annagiulia Pezzola

    Present address: PhD School, University of Macerata, Macerata, Italy

Authors and Affiliations

  1. Mathematics Division, School of Science and Technology, University of Camerino, Camerino, Italy

    Roberto Giambò & Annagiulia Pezzola

  2. INFN, Sezione di Perugia, 06123, Perugia, Italy

    Roberto Giambò

  3. Department of Marine Sciences, University of the Aegean, Lesbos, Greece

    John Miritzis

Authors
  1. Roberto Giambò
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  2. John Miritzis
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  3. Annagiulia Pezzola
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Correspondence to Roberto Giambò.

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Giambò, R., Miritzis, J. & Pezzola, A. Late time evolution of negatively curved FLRW models. Eur. Phys. J. Plus 135, 367 (2020). https://doi.org/10.1140/epjp/s13360-020-00370-3

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